D3Q27 Lattice-Boltzmann Navier-Stokes Solver

A high-performance 3D Lattice-Boltzmann solver for incompressible Navier-Stokes equations using GPU acceleration with WGPU and WGSL shaders.

Features

• D3Q27 Lattice Model: 27-velocity 3D lattice for accurate representation of fluid flow
• GPU Acceleration: WGPU-based compute shaders for high performance
• STL Geometry Input: Import complex geometries from CAD software
• ParaView Compatible Output: VTK format for professional visualization
• Configurable Parameters: JSON-based configuration for easy parameter adjustment
• Boundary Conditions: Support for inlet, outlet, and no-slip wall boundaries

Usage

# Build the project
cargo build --release

# Run a simulation
./target/release/lattice-boltzmann-rs config.json geometry.stl

Configuration File

The configuration file (JSON format) contains all simulation parameters:

{
  "domain": {
    "nx": 100,           // Grid points in x-direction
    "ny": 50,            // Grid points in y-direction  
    "nz": 50,            // Grid points in z-direction
    "dx": 0.01,          // Grid spacing in x (m)
    "dy": 0.01,          // Grid spacing in y (m)
    "dz": 0.01           // Grid spacing in z (m)
  },
  "physics": {
    "reynolds_number": 100.0,         // Reynolds number
    "inlet_velocity": [0.1, 0.0, 0.0], // Inlet velocity vector (m/s)
    "density": 1.0,                   // Fluid density (kg/m³)
    "viscosity": null                 // Optional: explicit viscosity (m²/s)
  },
  "simulation": {
    "max_iterations": 10000,          // Maximum number of time steps
    "convergence_tolerance": 1e-6,    // Convergence criterion
    "tau": null                       // Optional: explicit relaxation time
  },
  "output": {
    "output_directory": "./output",   // Output directory
    "output_frequency": 100,          // Output every N iterations
    "output_format": "vtk"           // Output format (vtk)
  }
}

STL Geometry

The solver accepts STL files containing the solid geometry. The STL file should:

• Be in ASCII or binary format
• Contain triangulated surfaces representing solid boundaries
• Be positioned within the computational domain defined in the config

Output Files

The solver generates VTK files compatible with ParaView:

• geometry.vtk: Visualization of the computational domain and boundary conditions
• output_XXXXXX.vtk: Transient flow solution files

Available Fields for Visualization

• Velocity: 3D velocity vector field (for streamlines)
• VelocityMagnitude: Scalar velocity magnitude
• Density: Fluid density field
• Pressure: Pressure field (derived from density)
• Vorticity: 3D vorticity vector (for flow structure analysis)
• NodeType: Boundary condition visualization (0=fluid, 1=solid, 2=inlet, 3=outlet)

Visualization in ParaView

1. Open ParaView
2. Load geometry.vtk to visualize the domain setup
3. Load output_*.vtk files as a time series
4. Create visualizations:
   • Streamlines: Use the Velocity vector field
   • Pressure contours: Use the Pressure scalar field
   • Velocity magnitude: Use VelocityMagnitude for speed visualization
   • Vortex structures: Use Vorticity magnitude or Q-criterion

Implementation Details

D3Q27 Lattice Model

The solver uses the 27-velocity 3D lattice model with:

• 1 rest particle (0,0,0)
• 6 face-connected neighbors (±1,0,0), (0,±1,0), (0,0,±1)
• 12 edge-connected neighbors
• 8 corner-connected neighbors

GPU Acceleration

The simulation runs entirely on the GPU using WGSL compute shaders:

• Collision shader: BGK collision operator with equilibrium distributions
• Streaming shader: Particle streaming to neighboring nodes
• Boundary shader: Implementation of boundary conditions

Boundary Conditions

• Inlet: Prescribed velocity using equilibrium distributions
• Outlet: Zero-gradient (Neumann) boundary condition
• Solid walls: Bounce-back boundary condition for no-slip walls
• Fluid: Standard LBM collision and streaming

Requirements

• Rust 1.70 or later
• GPU with WGPU support (DirectX 12, Vulkan, Metal, or WebGL)
• ParaView for visualization (free download from kitware.com)